# Thread: Question regarding Composite fxns with fractions

1. ## Question regarding Composite fxns with fractions

These are the two fxns

f(x) = (x+1)/(x-1)

g(x) = 1/x

I have to find f o g and f o f.

I tried to work it out but in f o g, it's too confusing what to do with the fraction in a fraction and in f o f it's in the num and denom.

I know the answers but not how to solve...

f o g = (1 + x)/ (1 - x)

f o f = X

2. Originally Posted by D-Rose
These are the two fxns

f(x) = (x+1)/(x-1)

g(x) = 1/x

I have to find f o g and f o f.

I tried to work it out but in f o g, it's too confusing what to do with the fraction in a fraction and in f o f it's in the num and denom.

I know the answers but not how to solve...

f o g = (1 + x)/ (1 - x)

f o f = X

$\displaystyle\ g(x)=\frac{1}{x}$

$\displaystyle\ f[g(x)]=\frac{g(x)+1}{g(x)-1}=\frac{\frac{1}{x}+1}{\frac{1}{x}-1}=\frac{\left(\frac{x+1}{x}\right)}{\left(\frac{1-x}{x}\right)}=\frac{1+x}{1-x}$

Try $f[f(x)]$

3. I don't understand how you went from Step 2 to 3...did something with the reciprocal of one of the fractions?

4. Originally Posted by D-Rose
I don't understand how you went from Step 2 to 3...did something with the reciprocal of one of the fractions?
Hi, you probably need some practice combining fractions.
Is the following ok?

$\displaystyle\frac{\frac{1}{x}+1}{\frac{1}{x}-1}=\frac{\frac{1}{x}+\frac{x}{x}}{\frac{1}{x}-\frac{x}{x}}=\frac{\left(\frac{1}{x}\right)}{\left (\frac{1}{x}\right)}\ \frac{1+x}{1-x}
$

5. Wow haha, I knew that but didn't think. Thanks!